Local aromaticity of the lowest-lying singlet States of [N]acenes (N = 6-9)

The local aromaticities of the six-membered rings in the two lowest-lying singlet states of [n]acenes (n = 6-9) have been assessed by means of three probes of local aromaticity based on structural, magnetic, and electron delocalization properties. Important differences between the local aromaticities of the closed-shell and diradical singlet electronic states are found. Thus, while the inner rings have the largest aromatic character in the closed-shell singlet states, the outer rings become the most aromatic for the diradical singlet states.     

Nonequilibrium dynamics in lattice ecosystems: Chaotic stability and dissipative structures

A generalized coupled map lattice (CML) model of ecosystem dynamics is presented. We consider the spatiotemporal behavior of a prey-predator map, a model of host-parasitoid interactions, and two-species competition. The latter model can show phase separation of domains (Turing-like structures) even when chaos is present. We also use this CML model to explore the time evolution and structural properties of ecological networks built with a set of N competing species. The May-Wigner criterion is applied as a measure of stability, and some regularities in the stable networks observed are discussed.     

Multipliers of Qs spaces and the corona theorem

For s>0, let Q_s be the space of all analytic functions onthe unit disc such that |f'(z)|²(1–|z|²)^s dA(z) isan s-Carleson measure. Here we prove that the corona theoremholds for the algebra of pointwise multipliers of Q_s.     

Kolmogorov Theorem revisited

Kolmogorov Theorem on the persistence of invariant tori of real analytic Hamiltonian systems is revisited. In this paper we are mainly concerned with the lower bound on the constant of the Diophantine condition required by the theorem. From the existing proofs in the literature, this lower bound turns to be of O(ε1/4), where ε is the size of the perturbation. In this paper, by means of careful estimates on Kolmogorov's method, we show that this lower bound can be weakened to be of O(ε1/2). This condition coincides with the optimal one of KAM Theorem. Moreover, we also obtain optimal estimates for the distance between the actions of the perturbed and unperturbed tori. We believe that some ideas contained in this paper may be used for improving several estimates in the general KAM context.     

Excess charge delocalization in organic and biological molecules: some theoretical notions

Theoretical and computational investigations of the excess charge distribution (ECD) in molecular complexes have attracted considerable attention as ECD is closely related to electronic properties of organic semiconductors, such as the efficiency of photoinduced charge separation in organic solar cells and charge transport in DNA and proteins. In this paper, we analyze the ECD in several representative models on the basis of ab initio and DFT calculations. We consider how changes in the reorganization energy, electronic coupling and charge transfer energy affect the ECD in the systems. In particular, we compare ECD in π stacks of polycyclic aromatic hydrocarbons and DNA nucleobases. While the π interaction between subunits in the systems is similar in both cases, ECD is quite different: the excess charge is found to be completely delocalized over the hydrocarbon stacks but strongly confined to a single nucleobase in DNA stacks. We also discuss the effects of conformational fluctuations on ECD in the stacks. Finally, ECD in amino acids and its dependence on the conformational changes are briefly considered.     

Selecting and adapting weekly work schedules with working time accounts: A case of a retail clothing chain

A case of selection and adaptation of weekly work schedules is presented. Weekly work schedules in two franchises of an important retail clothing chain have to be established. Working time accounts are used: each week, an employee can owe the company a certain number of hours or vice versa. Nevertheless, over a certain threshold, the hours have to be paid for by the company and the account balance returns to zero. A minimum and desired level of capacity of employees is contemplated. Hierarchically, the planned capacity must attempt to reach the minimum level; then it must fit a desired level as much as possible. At present, the task of allocation and the final adjustment of schedules is done manually, which is difficult, ineffective and often inaccurate. The procedure proposed is divided into two phases. Firstly, a work schedule, selected from a list, is assigned to each worker; a mixed linear program, followed by a local optimization process, is used. In the second phase, the work schedules are modified according to predefined rules: if there is a surplus of capacity, work schedules are reduced, and if there is a shortage, work schedules are extended. The company considers the results to be satisfactory.     

Studies on the Toxic Oil Syndrome: proposal of a mechanism for the thermal conversion of 3-N-phenylamino-1,2-propanediol esters into anilides under deodorisation conditions

A study on the reaction mechanism for the conversion of title esters, the species recognised as toxic biomarkers of the oil batches responsible for the Toxic Oil Syndrome, into the corresponding anilides under the thermal conditions of an oil deodorisation process was performed using experimental and computational techniques. The results obtained suggest a reaction course that includes two basic steps: an intramolecular process involving the reaction of the amine group of the diester derivative with the secondary ester of the same compound, followed by the attack of an aniline molecule to form the (E)-isomer of an imidic acid, which would finally tautomerise to give the final anilide.